Well, consider that starfleet put warp engines in pods on the end of tiny sticks to push a huge dish full of people from 0 to Warp 6 in a few seconds.
Never could figure out why the engines didn't just rip themselves off and go flying through subspace on their own.
But I maintain that the communicators were recharged with solar power or methane gas (the were worn on the backside after al). They needed more power than your Nokia phone to reach the ship in orbit.
Shalom.
In fairness, the cell-phone does have a very short range, and IS95 CDMA includes several measure to basically turn the phone off when it's not actually transmitting.
The Iridium handsets are a better analogue of the STrek communicators. Anybody know how long they last?